The present invention relates to medical imaging using gradient information. In particular, methods and systems for medical diagnostic imaging with computed spatial derivatives are provided. The computed spatial derivatives are used for volume rendering three dimensional images with shading or for other two- or three-dimensional imaging and image processing purposes.
Spatial gradients or derivatives are used in ultrasound imaging for various two- or three-dimensional applications. For example, filtering or motion tracking uses gradient information for two-dimensional ultrasound imaging. The gradients are calculated from scan converted data. Scan converted data is in a regular Cartesian grid for use by a display. Spatial derivatives of scan converted data are easily computed using filters. However, scan converted data may not be available for all applications using gradients, such as where the gradient information is used for processing data in an acoustic domain, such as in a spherical coordinate format associated with scanning. Since the resolution of ultrasound images is angle dependent and depth dependent, processing of scan converted ultrasound data may not be optimal as compared to processing of data in an acoustic domain. Changing the filtering parameters as a function of depth and scan line angle may be expensive or difficult to implement.
Gradients are used for shading representations of a volume. Volume rendering is a technique for visualizing 3D or 4D ultrasonic data on a computer screen. The viewer is assumed to view the data from an arbitrary vantage point. The computer screen is assumed to be between the viewer and the ultrasound data, with the computer screen being orthogonal to the viewing direction. Hypothetical rays are then cast from each pixel on the screen into the data volume. Data is re-sampled at regular intervals along the ray. The weighted sum of all data samples on each ray, after mapping using a suitable transfer function, is painted at each pixel of the screen, generating a volume rendered image of the 3D or 4D volume.
Volume rendering can be made more realistic by using shading. Shading assumes there are one or more light sources in the scene and each data sample on the ray has an associated gradient direction given by a unit vector. In the simplest lighting model, a Lambertian reflectance model is assumed, where the contribution by the light source is A cos θ, where A is the intensity of the light source and θ is the angle between the direction of the light source and the normal direction at the data sample. The contribution from the light source is combined into the weighted sum described above at each data sample along the ray during volume rendering, resulting in a more realistic-looking image. More complex lighting models also exist, such as Phong Specular Reflection Model, where the contribution from the light source takes the form A cos θ cos nα, where α is the angle between the direction of the viewer and the normal direction at the data sample and n is an integer. Note that the contributions from the light sources do not need to be recomputed when the viewing direction changes in the Lambertian model, in contrast to the Phone Specular Reflection model, where the contributions from the light sources are recomputed.
There are five basic steps to the process of volume rendering:                1. Segmentation        2. Gradient Computation        3. Re-sampling        4. Classification        5. ShadingIn the step of Segmentation, the data values in the volume are labeled. For example, the data values can be labeled as belonging to moving tissue, stationary tissue, blood, bone, different tissue types, B-mode, Doppler, etc. Segmentation basically subdivides the volume into regions of some homogeneous property. The regions can also overlap and may use probabilistic models. For example, a given data sample may contain 50% blood, 20% tissue and 30% bone.        
In the step of Gradient Computation, spatial gradients along three orthogonal directions are computed at each data sample. A unit vector is then generated by normalizing the spatial gradient vector for each data sample. In the step of Re-sampling, rays are cast from the pixels on the screen as described above and data and/or the normal vectors are re-sampled. In the step of Classification, the data values and/or the segmented data values are mapped using transfer functions and opacity functions. In the step of Shading, the contribution from the light sources are combined with the classified data values.
For three-dimensional (3D) imaging, volume rendering with shading uses gradients to modulate the voxel data using a hypothetical light coming from one or more light sources. To perform real time three-dimensional volume rendering with shading, spatial gradients along three dimensions are computed in real time. The three-dimensional gradients are calculated using finite impulse response filters convolved with the ultrasound data and indicate the strength and direction of spatial boundaries. The amount of light from a directional light source reflected to the viewer is determined as a function of these boundaries.
For 3D imaging, ultrasound or other medical imaging data is reconstructed or formatted onto a three-dimensional grid. For example, the three-dimensional grid represents a Cartesian coordinate format in three dimensions. The gradients for each location within the 3D grid are determined along three dimensions. The voxels of the 3D grid and associated gradients along three different dimensions are then resampled (i.e. interpolated) along the ray lines. Since three different gradient values are interpolated for each voxel, effectively four volumes are interpolated to the ray lines. However, interpolation of the gradients is expensive both in terms of computation and data access. When the three-dimensional data set is repetitively updated in real time, such as associated with four-dimensional ultrasound imaging, the directional gradient may be recomputed each time the data set changes. Additionally, each time the viewing direction changes, the gradients may be resampled.